Please find the value of the unknown in each of the following pictures
Answers
Solution:-
☘️Figure a :
∠A = 39°, ∠B = 90° and ∠C = a.
Let's have find ∠C !
We know that the sum of all angles of a triangle is 180°.
∠A + ∠B + ∠C = 180°
(Angle sum property)
→ 39° + 90° + a° = 180°
→ 129° + a = 180°
→ a = 180° – 129°
→ a = 51°
Therefore, the value of ∠C = 51°.
☘️Figure b :
∠A = 68°, ∠B = 2b° and ∠C = 64°
Let's find ∠B !
We know that the sum of all angles of a triangle is 180°.
∠A + ∠B + ∠C = 180°
(Angle sum property)
→ 68° + 2b° + 64° = 180°
→ 132° + 2b° = 180°
→ 2b° = 180° – 132°
→ 2b° = 48°
→ b = 48/2
→ b = 24°
Therefore, the value of ∠B = 24°
☘️Figure c :
∠A = 4c°, ∠B = 3c° and ∠C = 40°
Let's find ∠A and ∠B !
We know that the sum of all angles of a triangle is 180°.
∠A + ∠B + ∠C = 180°
(Angle sum property)
→ 4c° + 3c° + 40° = 180°
→ 7c° + 40° = 180°
→ 7c° = 180° – 40°
→ 7c° = 140°
→ c = 140/7
→ c = 20°
So,
∠A = 4c°
∠A = 4(20)
∠A = 80°
and, ∠B = 3c°
∠B = 3(20)
∠B = 60°
Therefore, the value of ∠A = 80° and ∠B = 60°.
☘️Figure d :
∠A = 3d°, ∠B = 4d° and ∠C = d°
Let's find all the angles !
We know that the sum of all angles of a triangle is 180°.
∠A + ∠B + ∠C = 180°
(Angle sum property)
→ 3d° + 4d° + d° = 180°
→ 8d° = 180°
→ d = 180/8
→ d = 22°
So, ∠A = 3d° → ∠A = 3(22.5) → ∠A = 67.5°
∠B = 4d° → ∠B = 4(22.5) → ∠B = 90.0°
∠C = d → ∠C = 22.5°
checking:
∠A + ∠B + ∠C = 180°
67.5° + 90.0° + 22.5° = 180°
180.0° = 180°
180° = 180°
LHS = RHS = 180°
Therefore, ∠A = 67.5°, ∠B = 90.0° and ∠C = 22.5°.
☘️Figure e :
∠A = 62°, ∠B = e°
and ∠C = ∠A (Because the given figure is an isosceles triangle and it has two sides equal)
So, ∠C = ∠A = 62°
Let's find ∠B !
We know that the sum of all angles of a triangle is 180°.
∠A + ∠B + ∠C = 180°
(Angle sum property)
→ 62° + e° + 62° = 180°
→ 124° + e° = 180°
→ e° = 180° – 124°
→ e° = 56°
Therefore, ∠B = 56° and ∠C = 62°
☘️Figure f :
The given figure is an Equilateral triangle. And it had all sides equal.
So, if ∠C = f° that means ∠A and ∠B also = f
Now,
We know that the sum of all angles of a triangle is 180°.
∠A + ∠B + ∠C = 180°
(Angle sum property)
f° + f° + f° = 180°
3f° = 180°
f° = 180/3
f = 60°
Therefore, ∠A = 60°, ∠B = 60° and ∠C = 60°.